You made a composite material, very much like fiberglass. It's a bunch of fibers in the form of a fabric, which provides the strength, and a solid matrix which causes the fibers to maintain their shape, so their strength is realized. I once reinforced the door of my perpetually broke girlfriend with a couple layers of brown paper, saturating it with waterproof glue...yeah, papier mache. It was amazingly sturdy and out-lasted our relationship.
I'd recommend trying again with the fiberglass, however. It's WAY stronger, only a bit more expensive if you don't waste materials, and just impervious to anything. If you REALLY want a strong part, don't discard the foam -- brush on a thin coat of epoxy (or polyester resin, or whatever you're using -- you can thicken it a bit with "microballoons" to make it thicker, which works better) to adhere the cloth to the foam, wet the fabric out, let it cure, dig out all but a 1/4" thickness or so of the foam, then glass the inside of the foam the same way. You won't believe how strong and lightweight a "foam-core sandwich" like this is, even with just a couple of very thin skins of composite.